The length of a pendulum that is equivalent to a rocking hemisphere

AI Thread Summary
The discussion revolves around determining the length of a simple pendulum equivalent to a rocking hemisphere with a radius r and mass M. The center of mass of the hemisphere is located at a distance of 3r/8 below the sphere's center. Participants express confusion over the derivation of the equations for period (T) and potential energy (V), suggesting that the denominator in the calculations may need to be adjusted from 5/8 to 3/8. There is an emphasis on the need for accurate geometric considerations in the solution process. The consensus leans towards the answer being 1.73r, but participants seek clarification on the derivations involved.
chriskh

Homework Statement


A solid sphere is cut in half and a homogeneous hemisphere of radius r and mass M is set upon a table(with its flat side up). The surface of the table is perfectly rough. The hemisphere rocks back and forth with small amplitude excursions from equilibrium. What is the length of an equivalent simple pendulum? Justify approximations. Note that the center of mass of a hemisphere is at a distance 3r/8 below the center of the sphere.

Homework Equations

The Attempt at a Solution

 
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Can you give it your best shot?
 
upload_2017-12-15_3-3-17.png

The answer should be 1.73r

I can't find what's wrong with my solution.
 

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I'm not sure about your derivation of either ##T## or ##V##. Can you justify those?

You may need to do some serious geometry!
 
I think you need 3/8 in the denominator instead of 5/8.
 
J Hann said:
I think you need 3/8 in the denominator instead of 5/8.
There's more than that is not right.
 
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